Peter E. Jupp

Estimating the Encounter Rate Variance in Distance Sampling

The dominant source of variance in line transect sampling is usually the encounter rate variance. Systematic survey designs are often used to reduce the true variability among different realizations of the design, but estimating the variance is difficult and estimators typically approximate the variance by treating the design as a simple random sample of lines. We explore the properties of different encounter rate variance estimators under random and systematic designs. We show that a design-based variance estimator improves upon the model-based estimator of Buckland et al. (2001, Introduction to Distance Sampling. Oxford: Oxford University Press, p. 79) when transects are positioned at random. However, if populations exhibit strong spatial trends, both estimators can have substantial positive bias under systematic designs. We show that poststratification is effective in reducing this bias.

How did they get here from there? Detecting changes of direction in terrestrial ranging

Efficient exploitation of large-scale space is crucial to many species of animal, but the difficulties of studying how animals decide on travel routes in natural environments have hampered scientific understanding of environmental cognition. Field experiments allow researchers to define travel goals for their subjects, but practical difficulties restrict large-scale studies. In contrast, data on natural travel patterns are abundant and easy to record, but hard to interpret without circularity and subjectivity when making inferences about when and why an animal began heading to a particular location. We present a method of determining objectively the point at which an animal’s travel path becomes directed at a location, for instance a distant feeding site, based on the statistical characteristics of its route. We evaluate this method and illustrate how it can be tailored to particular problems, using data that is (a) synthetic; (b) from baboons, where travel is from a single sleeping site in an overlapping home range, and (c) from chimpanzees, where sleeping sites are unlimited within a large territory. We suggest that this ‘change- point test’ might usefully become a routine first step in interpreting the decision- making behind animal travel under natural conditions.

Mathematical analysis of the alignment of guest molecules in solid one-dimensional inclusion compounds: the design of materials for applications in non-linear optics

Abstract A mathematical model of solid one-dimensional inclusion compounds is developed to assess the factors controlling the alignment of unsymmetrical guest molecules of the type XY within a tunnel host structure. Two models (uni-directional and bi-directional sequential models) are considered for the growth of the guest substructure within the host tunnel, and in these models the orientational characteristics of the guest molecules are considered to be functions of the energies of the X … X, X … Y and Y … Y guest-guest interactions and the host … XY and host YX interactions. The conditions, defined in terms of the relationships between these energies, that give rise to a parallel alignment of guest molecules within the host tunnel structure are derived. The fundamental understanding of the factors controlling the extent of parallel alignment of guest molecules within tunnel host structures developed in this paper is discussed in the context of the design of such inclusion compounds for applications in second harmonic generation and other second-order non-linear optical properties.

Sobolev tests of goodness of fit of distributions on compact Riemannian manifolds

Classes of coordinate-invariant omnibus goodness-of-fit tests on compact Riemannian manifolds are proposed. The tests are based on Gines Sobolev tests of uniformity. A condition for consistency is given. The tests are illustrated by an example on the rotation group S0(3).

A test of uniformity on shape spaces

A test of uniformity on the shape space Σmk is presented, together with modifications of the test statistic which bring its null distribution close to the large-sample asymptotic distribution. The asymptotic distribution under suitable local alternatives to uniformity is given. A family of distributions on Σmk, is proposed, which is suitable for modelling shapes given by landmarks which are almost collinear.

STOCHASTIC MODELS FOR GUEST-GUEST INTERACTIONS IN ONE-DIMENSIONAL INCLUSION COMPOUNDS

The intrinsic relative preferences of X…X, X…Y and Y…Y interactions between functional groups X and Y can be obtained by considering a set of one–dimensional inclusion compounds containing guest molecules of two (or more) of the types X X, X Y, and Y Y, with the molar ratios of these types of guest molecule differing between the members of the set. Limited information on the relative preferences of these interactions can also be obtained by considering a one–dimensional inclusion compound containing only guest molecules of the type X Y. Two probabilistic models are presented for the sequence of oriented guest molecules in a tunnel of a one–dimensional inclusion compound containing these different types of guest molecule. One model is specified by a Markov chain and is appropriate when the guest molecules are introduced sequentially into the tunnel. The other model is specified by interaction between a guest molecule and both of its neighbours, and is appropriate when the guest molecules are introduced simultaneously into the tunnel. For both models, functional relationships are obtained between the molar ratios of the different types of guest molecule and the ratios of the numbers of X…X, X…Y and Y…Y interactions, all of which can, in principle, be determined experimentally. The intrinsic parameters, which represent the relative energies of these interactions, can be estimated using the corresponding regression equations.

Residuals for directional data

Various types of residual are proposed for use with directional data. Asymptotic distributions are given for large sample sizes and for concentrated error distributions. A form of residual plot is suggested and is illustrated with some practical examples.

Data-driven Sobolev tests of uniformity on compact Riemannian manifolds

Data-driven versions of Sobolev tests of uniformity on compact Riemannian manifolds are proposed. These tests are invariant under isometries and are consistent against all alternatives. The large-sample asymptotic null distributions are given.

Yokes and symplectic structures

Abstract A relationship between yokes and symplectic forms is established and explored. It is shown that normalised yokes correspond to certain symplectic forms. A method of obtaining new yokes from old is given, motivated partly by the duality between the Hamiltonian and Lagrangian formulations of conservative mechanics. Some variants of this construction are suggested.

A theoretical framework for the experimental determination of host–guest interaction energies in solid inclusion compounds

A mathematical model is developed to provide the framework of an experimental approach for determining host–guest interaction energies in solid inclusion compounds with one-dimensional tunnel host structures. The approach considers the competitive inclusion of two different types of potential guest molecules X(S)qX and X(S)rX (q≠r) within the tunnel host structure, where X represents a given type of end group (e.g., CH3, halogen, etc.) and S represents an appropriate spacer unit (e.g., CH2, CH, etc.). Sequential and simultaneous models for the growth of the guest substructure within the host tunnel are considered. The relative proportions (m and 1−m) of the two types of guest molecule included within the host tunnel depend on the relative proportions (γ and 1−γ) of the two types of guest molecule in the external “pool” of potential guest molecules and the relative “affinities” (χ and 1/χ) of the host tunnel structure for including the two different types of guest molecule. Expressions linking χ, m, and γ ...